CATASTROPHE MODELING:
A NEW APPROACH TO
MANAGING RISK
Huebner International Series on
Risk, Insurance, and Economic
Security
J. David Cummins, Editor
The Wharton School
University of Pennsylvania
Philadelphia, Pennsylvania, USA
Series Advisors:
Dr. Phelim P. Boyle
University of Waterloo, Canada
Dr. Jean Lemaire
University of Pennsylvania, USA
Professor Akihiko Tsuboi
Kagawa University, Japan
Dr. Richard Zeckhauser
Harvard University, USA
Other books in the series:
Cummins,
J. David and Derrig, Richard A.: Classical
Insurance Solvency Theory
Borba, Philip S. and Appel, David: Benefits, Costs, and
Cycles in Workers’ Compensation
Cummins, J. David and Derrig, Richard A.: Financial Models
of
Insurance Solvency
Williams, C. Arthur: An International Comparison of
Workers’ Compensation

HOWARD
KUNREUTHER
Managing Editors
Risk Management and Decision Processes Center
The Wharton School
University of Pennsylvania
assisted by
CHANDU C. PATEL, FCAS, MAAA (EDITOR)
Springer
eBook ISBN: 0-387-23129-3
Print ISBN: 0-387-23082-3
Print ©2005 Springer Science + Business Media, Inc.
All rights reserved
No part of this eBook may be reproduced or transmitted in any form or by any means, electronic,
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©2005 Springer Science + Business Media, Inc.
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Contents
Preface and Acknowledgements
xiii
Prelude xvii
PART I - Framework for Risk Management
Using Catastrophe Models
1
1
Introduction: Needs, Stakeholders, and
Government Initiatives

1.4
1.5
Summary of Chapter
References
10
10
11
11
12
13
13
15
19
20
2
An Introduction to Catastrophe Models and Insurance
Patricia Grossi, Howard Kunreuther, Don Windeler
23
2.1
2.2
2.3
2.4
History of Catastrophe Models
Structure of Catastrophe Models
Uses of a Catastrophe Model for Risk Management
Derivation and Use of an Exceedance Probability
Curve
23
26
27

40
41
PART II
–
Natural Hazard Risk Assessment
43
3
The Risk Assessment Process: The Role of Catastrophe
Modeling in Dealing with Natural Hazards
Mehrdad Mahdyiar, Beverly Porter
45
3.1
3.2
Introduction
Hazard Module
45
47
3.2.1
3.2.2
3.2.3
3.2.4
Locations of Potential Future Events
Frequency of Occurrence
Parameterizing Severity at the Hazard’s Source
Parameters for Local Intensity and Site Effects
47
51
54
55
58

70
70
74
74
76
78
79
79
82
89
90
Introduction
Classifications of Uncertainty
Sources of Uncertainty
Representing and Quantifying Uncertainty
4.4.1
4.4.2
4.4.3
Logic Trees
Simulation Techniques
Uncertainty and the Exceedance Probability Curve
4.5
Case Studies in Uncertainty
4.5.1
4.5.2
Hurricane Hazard: Florida
Earthquake Hazard: Charleston, South Carolina
4.6
4.7
Summary and Conclusions

5.5.2
5.5.3
Formation of the CEA
Rate-Setting Procedures
Future Research Issues
108
109
115
115
5.6
Open Issues for Using Catastrophe Models to
Determine Rates
5.7
5.8
Summary
References
117
118
6
Insurance Portfolio Management
Weimin Dong, Patricia Grossi
119
119
120
120
121
124
125
126
127

Impact of Correlation
6.5
6.6
Summary
References
5.3.1
5.3.2
A Simple Rate Making Model
Differentiating Risk
viii
7
Risk Financing
David Lalonde
135
7.1
7.2
135
136
137
138
139
139
141
143
145
156
158
159
160
160

7.5.4
7.5.5
7.5.6
Develop Risk Management Alternatives
Evaluate Alternative Strategies
Select, Implement, and Monitor Strategy
7.6
7.7
Summary
References
161
161
162
163
164
PART IV
–
Risk Management Strategies
Using Catastrophe Models
165
8
The Impact of Mitigation on Homeowners and Insurers:
An Analysis of Model Cities
Paul Kleindorfer, Patricia Grossi, Howard Kunreuther
167
8.1
8.2
8.3
Introduction
Framework of Analysis

Factors Influencing Mitigation Adoption Decisions
ix
8.5.2
The Interaction of Mitigation Decisions and Insurance
Decisions
180
8.6
Implications for Workable Public-Private Partnerships
8.6.1
8.6.2
8.6.3
Role of Building Codes
Long-Term Mitigation Loans
Lower Deductibles Tied to Mitigation
181
183
184
184
186
187
8.7
8.8
Conclusions
References
9
The Impact of Risk Transfer Instruments:
An Analysis of Model Cities
Howard Kunreuther, Paul Kleindorfer, Patricia Grossi
189
9.1

9.5.4
Multi-Region Catastrophe Bonds
9.6
9.7
9.8
Extensions of the Analysis
Conclusions
References
204
205
206
208
10
Extending Catastrophe Modeling To Terrorism
Howard Kunreuther, Erwann Michel-Kerjan,
Beverly Porter
209
10.1
10.2
10.3
Introduction
September 11, 2001: Impacts on Terrorism Insurance
The Nature of Terrorism Coverage
10.3.1
10.3.2
10.3.3
Insurability Issues
Expanding Capacity Through Catastrophe Bonds
Potential Role of Catastrophe Bonds
10.4

10.7
Low Insurance Demand for Terrorism Coverage
10.7.1
10.7.2
Empirical Evidence
Heuristics and Biases
10.8
218
219
222
222
224
226
227
227
228
229
229
229
230
232
235
241
Future Research Directions
10.8.1
10.8.2
10.8.3
Vulnerability Analyses
Risk Perception
Interdependencies

risks, three leading firms [AIR Worldwide, EQECAT and Risk Management
Solutions (RMS)] on modeling the risks using information technology, and
the development of new strategies by insurers, reinsurers and financial
institutions for managing catastrophic risks.
Over the past 8 years, representatives from all these constituencies
have worked together as part of the Wharton Managing Catastrophic Risks
project to examine the role of catastrophe modeling in assessing and
managing natural disaster risk. This book is truly a joint effort with the
modeling firms and reflects the critical commentary and evaluations from key
individuals in insurance and reinsurance companies as well as financial
institutions who provided funds for the research activities.
From 1996 through 2001, the project was a joint venture between the
Wharton Financial Institutions Center (WFIC) and the Wharton Risk Center.
We want to express our deep appreciation to Anthony Santomero, director of
the WFIC during the first five years of the project, Peter Burns, project
manager, and Steve Levy, project coordinator, during this period. Thanks also
go to Franklin Allen, Richard Herring and Carol Leisenring who assumed
leadership positions at the WFIC after Anthony Santomero and Peter Burns
moved on from the Wharton School in 2000.
From the outset, our goal was to undertake state-of the-art research on
the role of risk assessment in developing meaningful strategies for managing
catastrophic risks. Although our focus was on natural hazards, we viewed the
project as one that could be applied to a wide variety of extreme events. In
fact, since 2002 the Managing Catastrophic Risks project has morphed into
the Managing Extreme Events project, which is one of the major ongoing
activities at the Wharton Risk Center.
To ensure the highest scientific standards, we formed a Technical
Advisory Committee (TAC) whose role was to provide detailed commentary
on the models developed by AIR Worldwide, EQECAT and Risk
xiv

There are numerous other individuals and firms who played a key role
in this effort. Jim Tilley from Morgan Stanley and Jerry Isom from CIGNA
(now ACE) convinced their organizations to provide initial seed funding for
the project. Other sponsors included American Re, General Re, Goldman
Sachs, Japan Property and Casualty Association, State Farm, Swiss Re, and
Tokio Marine. A number of individuals from these organizations provided us
with extremely helpful comments at various stages of the project. They
include: James Ament (State Farm), David Durbin (Swiss Re), Carl Hedde
(American Re), Robert Irvan (CIGNA/ACE), Jeff Warren (General Re),
Gordon Woo (Risk Management Solutions), Yuichi Takeda (Tokio Marine).
American Re (Carl Hedde, Mark Bove, and Hjortur Thraisson) provided key
information on historic losses. Goldman Sachs (Vivek Bantwal and Ohi
Akhigbe) also provided helpful comments on the current state of catastrophe
xv
bonds and other new financial instruments.
Special thanks go to the leadership in all three modeling firms for
agreeing to share their software with the Wharton team and to open their
doors to a dialog with academia: Karen Clark from AIR Worldwide; Dennis
Kuzak from EQECAT; and Tom Hutton, Haresh Shah, and Terry van Gilder,
who were at Risk Management Solutions when the project started.
The research on this book occurred over a span of almost 9 years, so
there have been a number of individuals who have played a key role in
helping to undertake the research that forms the basis for each of the chapters.
At the beginning of each chapter, we list the principal authors who took the
lead in writing the material, but there are others who played a role in
providing data for the various chapters. In particular, we want to thank Vivek
Bantwal, Jessica Binder and Jaideep Hebbar, three remarkable undergraduate
students at Wharton, who were indefatigable in their efforts working with the
modeling groups. Without their assistance, Chapters 8 and 9 in the book could
not have been written. Paul Kleindorfer, co-director of the Wharton Risk

Professor at Southern Methodist University and finally to her current position
at Risk Management Solutions. On September 3, 2001, Howard Kunreuther
began a one-year sabbatical at the Earth Institute (Columbia University) and
has been involved in terrorism research ever since September The last
chapter of the book reflects the broader objectives of catastrophe modeling by
applying the concepts from natural hazards to this risk.
Our families have been part of the process from the very beginning
and our spouses, Mohan Balachandran and Gail Loeb Kunreuther, deserve
special thanks for their encouragement and understanding.
Patricia Grossi
Howard Kunreuther
Prelude
The aftermath of a natural disaster, such as an earthquake, flood,
hurricane, can be devastating. There is a tremendous sense of personal as
well as economic loss. Immediately following the disaster, the actual
devastation as well as media coverage related to the event causes the affected
individuals as well the general public to be keenly aware of the risk of
catastrophes. Unfortunately, this awareness often fades with time and the
importance of being prepared is often forgotten. There are, however, a large
number of individuals who spend a great deal of time and energy modeling
natural disasters and enlightening others on ways in which their impact can be
managed.
The goal of this book is to bring the reader up to date on recent
developments in the nature and application of catastrophe models used to
manage risk from natural disasters. It describes current and potential future
uses of such models. The book emphasizes natural disasters, but also
discusses application of the models to the terrorist attacks of September 11,
2001. The book is targeted to individuals concerned with monitoring and
managing the impact of catastrophe risks. For example:
Senior insurance and reinsurance managers can gain insight into the

Chapter 4 discusses the treatment of uncertainty in a catastrophe
model. Catastrophe modeling is an evolving science; there are assorted
interpretations and approaches to the modeling process. Differences in the
output from competing catastrophe models are presented for hurricane and
earthquake risk. Using the Charleston, South Carolina region as an example,
the chapter highlights how uncertainty in modeling risks affects estimates of
future losses.
Part III examines how catastrophe modeling currently aids insurers
and other stakeholders in managing the risks from natural hazards. After a
general overview of current practices used by insurers, specific examples of
risk management strategies are discussed in Chapters 5 though 7. Chapter 5
focuses on the actuarial principles for insurance rate making. Special
emphasis is given to the role of catastrophe modeling in earthquake risk
classification and rate setting for residential structures in the state of
California.
Chapter 6 focuses on the role of catastrophe modeling in quantifying
an insurer’s portfolio risk. One of an insurer’s principal concerns when
constructing a portfolio of risks is to reduce the possibility of unusually large
losses. Special attention is given to ways that models can address uncertainty
issues and reduce the chances of highly correlated losses in an insurer’s
portfolio.
Chapter 7 provides a comprehensive discussion of risk financing for
an organization and the regulatory basis for the design of risk transfer
instruments. The chapter illustrates the role that catastrophe modeling plays in
evaluating these financing schemes and discusses the reasons why there has
been limited interest by investors in utilizing new financial instruments.
xix
Part IV illustrates how catastrophe models can be utilized in
developing risk management strategies for natural disasters and terrorism. In
Chapter 8, insurers consider a specific risk management strategy – requiring

CATASTROPH
E
MODELS
Part I of this book is an introduction to natural hazards and
catastrophe risk management. Chapter 1 discusses the history of natural
disaster loss and introduces the stakeholders who manage catastrophe risk,
along with their motivations and relationships to one another. The chapter
also discusses the role of the public and private sectors in managing risk.
Chapter 2 turns to the development of catastrophe models and the use of
insurance in managing catastrophe risk. The concept of an exceedance
probability curve is introduced. This is a key element used throughout the
book for communicating risk to a stakeholder. Finally, a conceptual
framework is presented that illustrates the critical role that catastrophe
modeling plays in managing risk.
San Francisco, California, Earthquake April 18, 1906. Fault trace 2 miles north of the
Skinner Ranch at Olema. View is north. Plate 10, U.S. Geological Survey Folio 193;
Plate 3-A, U.S. Geological Survey Bulletin 324.
This page intentionally left blank
Chapter 1 – Introduction: Needs, Stakeholders, and
Government Initiatives
Major Contributors:
Patricia Grossi
Howard Kunreuther
1.1
Need to Manage Risk
The problem of preparing for a natural disaster is not a new one.
Around the world and particularly in the more-developed countries,
governments, individuals and corporations know they should prepare for a
“big earthquake” or a “large hurricane” or an “extensive flood.” Yet, they
often do not take the necessary steps to prepare for a disaster. Only after a

during the 1990’s exceeded $40 billion dollars each year with the exception of
1997. Losses were as high as $170 billion in 1995, primarily due to the large-
scale earthquake that destroyed portions of Kobe in Japan in January of that
year. Insured losses matched this growth during the same timeframe.
The volatility and trend in losses can be seen in the United States as
well. Figure 1.2(a) and Figure 1.2(b) show the economic and insured losses
from significant United States catastrophes from 1950 through 2002 with
losses adjusted to 2002 dollars. U.S. catastrophes are deemed significant when
there is an adjusted economic loss of at least $1 billion and/or over 50 deaths
attributed to the event (American Re, 2002).
There are peaks in losses due to catastrophic events, as in worldwide
losses (most prominently in 1989, 1992, and 1994), and the upward trend over
the past 50 years is evident when broken down by decade, as seen in Figure
1.2(b). The losses from individual disasters during the past 15 years are an
order of magnitude above what they were over the previous 35 years.
Furthermore, prior to Hurricane Hugo in 1989, the insurance industry in the
United States had never suffered a loss of over $1 billion from a single
disaster. Since 1989, numerous disasters have exceeded $1 billion in insured
losses. Hurricane Andrew devastated the coastal areas of southern Florida in
August 1992, as well as damaging parts of south-central Louisiana causing
$15.5 billion in insured losses. Similarly, on the west coast of the United
States, insured losses from the Northridge earthquake of January 1994
amounted to $12.5 billion.
Residential and commercial development along coastlines and areas
with high seismic hazard indicate that the potential for large insured losses in
the future is substantial. The ten largest insured property losses in the United
States, including the loss from 9/11, are tabulated in Table 1.1 adjusted to
2001 dollars (Insurance Information Institute, 2001). The increasing trend for
catastrophe losses over the last two decades provides compelling evidence for
the need to manage risks both on a national, as well as on a global scale.